GCF of 8/31, 52/18, 14/918, 320/415
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8/31, 52/18, 14/918, 320/415 i.e 2/11810070 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8/31, 52/18, 14/918, 320/415.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 8/31,52/18,14/918,320/415?
Given fractions are 8/31,52/18,14/918,320/415
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 8/31,52/18,14/918,320/415, numerators are 8,52,14,320
Denominators are 31,18,918,415
The GCF of 8,52,14,320 is 2 .
LCM of 31,18,918,415 is 11810070.
The greatest common factor of 8/31,52/18,14/918,320/415 = [GCF of 8,52,14,320]/[LCM of 31,18,918,415]= 2/11810070
Therefore, the GCF of 8/31,52/18,14/918,320/415 is 2/11810070.
To find the highest common factor of 8,52,14,320, we have to find the factors of both numbers and list the highest common factor.
The factors of 8 are 1, 2, 4, 8
The factors of 52 are 1, 2, 4, 13, 26, 52
The factors of 14 are 1, 2, 7, 14
The factors of 320 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320
The HCF of 8,52,14,320 is 2.
Lets's calculate GCF of 8,52,14,320
| 2 | 8, 52, 14, 320 |
| 4, 26, 7, 160 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 8,52,14,320 By Matching Biggest Common Factor Method
Now, list down the factors of 8
:1,2,4,8
Now, list down the factors of 52
:1,2,4,13,26,52
Now, list down the factors of 14
:1,2,7,14
Now, list down the factors of 320
:1,2,4,5,8,10,16,20,32,40,64,80,160,320
Greatest Common Factor
We found the factors 8,52,14,320 . The biggest common factor number is the GCF number.
So the greatest common factor 8,52,14,320 is 2.
Lets's calculate LCM of 31,18,918,415
| 2 | 31, 18, 918, 415 |
| 3 | 31, 9, 459, 415 |
| 3 | 31, 3, 153, 415 |
| 31, 1, 51, 415 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 31 x 1 x 51 x 415 = 11810070
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/11810070
Therefore, the GCF of Fractions 8/31,52/18,14/918,320/415 is 2/11810070
Least Common Multiple of 31,18,918,415 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 31,18,918,415 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,18,918,415) = 1
common factors(in case of two or more numbers have common factors) = 18
GCF(31,18,918,415) x common factors =1 x 18 = 18
LCM(31,18,918,415) = ( 31 × 18 × 918 × 415 ) / 18
LCM(31,18,918,415) = 212581260 / 18
LCM(31,18,918,415) = 11810070
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FAQs on GCF of Fractions of 8/31, 52/18, 14/918, 320/415
1. What is the HCF of 8,52,14,320?
The HCF of 8,52,14,320 is 2
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 8/31, 52/18, 14/918, 320/415?
Answer: GCF of Numerators as per given numbers 8/31, 52/18, 14/918, 320/415 is
GCF of Numerators i.e. for 8,52,14,320 is 2
LCM of denominators i.e. for 31,18,918,415 is 11810070.
Thus, GCF of Fractions is 2/11810070.Finally, GCF of Fractions for 8/31, 52/18, 14/918, 320/415 is 2/11810070.